def effective_mass(p1, p2):
if (p_space_grid == 'cartesian'):
p_x = p1
p_y = p2
theta = af.atan(p_y / p_x)
elif (p_space_grid == 'polar2D'):
# In polar2D coordinates, p1 = radius and p2 = theta
r = p1
theta = p2
else:
raise NotImplementedError('Unsupported coordinate system in p_space')
p_F = fermi_momentum_magnitude(theta)
if (fermi_surface_shape == 'hexagon'):
n = 6 # No. of side of polygon
#mass = mass_particle * polygon(n, theta, rotation = np.pi/6)
mass = (p_F / fermi_velocity) * polygon(n, theta, rotation=np.pi / 6)
# Note : Rotation by pi/6 results in a hexagon with horizontal top & bottom edges
elif (fermi_surface_shape == 'circle'):
# For now, just return the free electron mass
#mass = mass_particle
mass = p_F / fermi_velocity
return (mass)
def fermi_momentum_magnitude(theta):
if (fermi_surface_shape == 'circle'):
if (dispersion == 'linear'):
p_f = initial_mu / fermi_velocity # Fermi momentum
elif (dispersion == 'quadratic'):
p_f = 0.015 # numerical value set by mu/v_F, with mu = 0.015 and v_F = 1
elif (fermi_surface_shape == 'hexagon'):
n = 6 # No. of sides of polygon
if (dispersion == 'linear'):
p_f = (initial_mu / fermi_velocity) * polygon(
n, theta, rotation=np.pi / 6)
elif (dispersion == 'quadratic'):
p_f = 0.015 * polygon(
n, theta, rotation=np.pi / 6
) # numerical value set by mu/v_F, with mu = 0.015 and v_F = 1
# Note : Rotation by pi/6 results in a hexagon with horizontal top & bottom edges
else:
raise NotImplementedError('Unsupported shape of fermi surface')
return (p_f)
def fermi_momentum_magnitude(theta):
if (fermi_surface_shape == 'circle'):
p_f = initial_mu/fermi_velocity # Fermi momentum
elif (fermi_surface_shape == 'hexagon'):
n = 6 # No. of sides of polygon
p_f = (initial_mu/fermi_velocity) * polygon(n, theta, rotation = np.pi/6)
# Note : Rotation by pi/6 results in a hexagon with horizontal top & bottom edges
#TODO : If cartesian coordinates are being used, convert to polar to calculate p_f
else :
raise NotImplementedError('Unsupported shape of fermi surface')
return(p_f)
#f_at_desired_q = np.reshape((dist_func - \
# dist_func_background)[q1_position, q2_position, :],
# [N_p2, N_p1]
# )
#print ("f at desired q : ", dist_func[q1_position, q2_position, :].shape)
print("norm : ", norm_factor)
radius = f.copy()
theta = p2.copy()
n = 6 # Number of sides of polygon
r_bg = 5.
weight = polygon(n, af.from_ndarray(theta),
rotation=np.pi / 6).to_ndarray()
x = (radius + r_bg) * np.cos(theta) * weight
y = (radius + r_bg) * np.sin(theta) * weight
x_bg = r_bg * np.cos(theta) * weight
y_bg = r_bg * np.sin(theta) * weight
# To remove the discontinuity at -pi/pi
x = np.insert(x, -1, x[0])
y = np.insert(y, -1, y[0])
print('p2 : ', p2.shape)
#pl.plot(p2, f_at_desired_q)
pl.plot(x, y, color='r', linestyle='-', lw=3)
pl.plot(x_bg, y_bg, color='k', alpha=0.5, lw=3)
import arrayfire as af
import pylab as pl
import domain
from bolt.src.electronic_boltzmann.utils.polygon import polygon
p2_start = -np.pi
p2_end = np.pi
N_p2 = domain.N_p2
theta = \
p2_start + (0.5 + np.arange(N_p2))*(p2_end - p2_start)/N_p2
theta = af.from_ndarray(theta)
hexa = polygon(6, theta, rotation=np.pi / 6)
hexa = hexa.to_ndarray()
#pl.polar(theta, hexa)
#pl.plot(theta, hexa * np.cos(theta))
#pl.plot(theta, hexa * np.sin(theta))
pl.gca().set_aspect(1)
pl.plot(hexa * np.cos(theta), hexa * np.sin(theta))
#p_hat_0_old = np.loadtxt("P_hat_0_old.txt")
#p_hat_1_old = np.loadtxt("P_hat_1_old.txt")
#p_hat_0 = np.loadtxt("P_hat_0.txt")
#p_hat_1 = np.loadtxt("P_hat_1.txt")